Problem: Solve for $x$ and $y$ using elimination. ${-3x-2y = -24}$ ${3x+5y = 51}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $3y = 27$ $\dfrac{3y}{{3}} = \dfrac{27}{{3}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-3x-2y = -24}\thinspace$ to find $x$ ${-3x - 2}{(9)}{= -24}$ $-3x-18 = -24$ $-3x-18{+18} = -24{+18}$ $-3x = -6$ $\dfrac{-3x}{{-3}} = \dfrac{-6}{{-3}}$ ${x = 2}$ You can also plug ${y = 9}$ into $\thinspace {3x+5y = 51}\thinspace$ and get the same answer for $x$ : ${3x + 5}{(9)}{= 51}$ ${x = 2}$